How do you solve the system of equations #5x - 6y = 9# and #5x + 2y = 19#?

1 Answer
Mar 22, 2017

Answer:

The final solution is #x = 3 3/10# and #y = 1 1/4# using substitution to solve the system of equations.

Explanation:

We notice that in both equations, there is a #5x#. This suggests using elimination to solve the equations.

Since the equations have the same term with one of the variables (#5x#), we can subtract the two equations to eliminate #x# and leave one equation to solve for #y#. Subtracting the first equation from the second and solving gives us:

#2y - (-6y) = 19 - 9#

#8y = 10#

#y = 5/4#

Now, we can simply substitute the value of #y# into any of the 2 equations to solve for #x#. Substituting into the second equation and solving, we get:

#5x + 2(5/4) = 19#

#5x + 5/2 = 19#

#5x = 33/2#

#x = 33/10#

So, the answer to the equations is #x = 3 3/10# and #y = 1 1/4#.